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  • Provide solution for RD Sharma maths class 12 chapter 9 Differentiability exercise Fill in the blanks question 14

Provide solution for RD Sharma maths class 12 chapter 9 Differentiability exercise Fill in the blanks question  14

Answers (1)

Answer: [0]

Given: f(x)=|\sin x|

Solution: f(x)=|\sin x|

f(x)= \begin{cases}\sin x & x \geq 0 \\ -(\sin x) & x<0\end{cases}

\begin{aligned} &R f^{\prime}(0)=\lim _{h \rightarrow 0^{+}} \frac{f(0+h)-f(0)}{h} \\\\ &=\lim _{h \rightarrow 0^{+}} \frac{|\sinh |-0}{h} \\\\ &=\lim _{h \rightarrow 0^{+}} \frac{\sinh }{h} \\\\ &=1 \end{aligned}

\begin{aligned} &\text { As } h \rightarrow 0^{+},|\sinh |=\sinh \\\\ &\begin{aligned} L f^{\prime}(0) &=\lim _{h \rightarrow 0^{-}} \frac{f(0-h)-f(0)}{h} \\\\ &=\lim _{h \rightarrow 0^{-}} \frac{|\sinh |-0}{h} \end{aligned} \end{aligned}

              \begin{aligned} &=\lim _{h \rightarrow 0^{-}} \frac{(-\sinh )}{h} \\ &=-1 \end{aligned}

\begin{aligned} &\text { As } h \rightarrow 0^{-},|\sinh |=-\sinh \\\\ &\text { So, } R f^{\prime}(0) \neq L f^{\prime}(0) \end{aligned}

Hence, f(x)=|\sin x| is not differentiable at x=0.

 

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